Recent content by atqamar

Oh stupid me. That wasn't tough at all. Thanks!

I'm having a hard time evaluating this integral. A Gaussian pulse \psi (y,t) = Ae^{-( \frac{y-ct}{a} )^2} is traveling in an infinite string of linear mass density \rho, under tension T. I know the Kinetic Energy is the integral of the partial: \frac{\rho}{2} \int_{-\infty}^{\infty}...

Thanks a lot Gib Z! That helped immensely.

Certainly, these are all improper integrals. But my question is whether the above integrals would converge or diverge. Intuitively/Geometrically, they should converge; but like I said, once the improper integral is carried out, one has to deal with infinities.

If an odd function has an infinite discontinuity in its domain, can it be integrated (such that a convergent finite emerges) with that domain included? For example: \int_{-1}^2 \frac{1}{x^{-3}} dx. Intuitively, it can be simplified to \int_1^2 \frac{1}{x^{-3}} dx and thus the infinite...

a) V_i_c_e = V_e_n_t_i_r_e _b_a_l_l - V_i_r_o_n = \frac{4\pi}{3}(4+w)^3 - \frac{4\pi}{3}(4)^3 = \frac{4\pi}{3}((4+w)^3 - (4)^3) Differentiate with respect to time: \frac{dV_i_c_e}{dt} = \frac{4\pi}{3}(3(4+w)^2\frac{dw}{dt}) -10 = \frac{4\pi}{3}(3(4+2)^2\frac{dw}{dt}) \frac{dw}{dt} =...

a) You must realize that the rate of melting given is not for the iron ball + ice... It is only for the ice. Write a formula for V_i_c_e, given the total radius r_b_a_l_l_+_i_c_e is 4 + w; when w is the width (thickness) of the ice. Then differentiate with respect to time. b) This is a bit more...

Just an idea: P is a function of k_1, k_2, and k_3. So the multivariable formula is in the form P(k_1, k_2, k_3) = ak_1 + bk_2 + ck_3. If you have many values of P and k in the formula P(k) = ak, you would run a single variable regression on the data to find a reasonable value of a. Thus...

Thank you very much for the insight Office_Shredder. Now I can make only the possible arrangements, and the remaining arrangements of the 126 will be the ones that don't create a "line of 3 squares".

The fact that _9C_5=126 shows that there are a total of 126 possible ways a group of five squares can be selected at random. Now how many of these 126 arrangements of squares contain at least one "line of 3 squares"? Do I have to draw all the possibilities (and consider some of the possibilities...

I considered that, but you are not choosing 3 squares at a time... but instead, you are choosing a group of 5 squares. And from these 5 squares, what is the probability that there is a "line of 3 squares".

Consider a 3-by-3 square grid. Suppose you pick 5 of the squares at random. What is the probability that at least 1 line of 3 squares is formed? (3 diagonal squares is NOT a line). I do know that there are 6 combinations of lines that are possible. After that, I'm not sure how to follow along...

GrafEq is amazing at graphing complicated implicit or explicit functions, and has many, many trigonometric functions, gamma function, etc... built in. Play around with it a bit, and you'll be a pro. ftp://ftp.peda.com/grafeq32.exe

Glad to see you've accepted the fact that log(-1) is an imaginary number. Try finding what that imaginary number is. Use Euler's identity: e^{\pi i}=-1.

I graphed y1=nDeriv((2^x)/((x^2)-1), x, x) and it came out fine. The window is set to standard. By the way, when using the nDeriv function, here is how you set it up: nDeriv(function,variable,value) If you are on the home screen, and you want to calculate the derivative of a specific value to a...